MYTUTOR SUBJECT ANSWERS

366 views

How do you find the area between two lines?

First, find the x coordinates of where the lines intersect by setting the equations of the lines equal to each other. Then solve the quadratic (or polynomial) equation. Next, integrate both lines individually with the limits being the x coodinates of the intersection. Then subtract the area of the lower line from the area of the upper line to find the area between the two.

For example:

Find the area between y=4x and y=x- 2x + 5.

To find the x coordinates, set them equal to each other and solve.

So... 4x = x- 2x + 5 => 0 = x- 6x + 5. Thus using either the quadratic formula or factorising, we find that these lines intesect when x=1 and x=5

Next, we need to integrate the lines between the limits found.

So... y=4x integrates to => [2x2] and when plugging in x=5, we get 50 and x=1 gives us 2. Thus the area of y=4x bound by the x axis, x=1 and x=5 is 50-2 = 48.

Similarly, y=x- 2x + 5 integrates to => [x3/3 - x2 + 5x]. Again, we put in x=5 and it gives 125/3 and x=1 gives us 13/3. Thus the area of y=x- 2x + 5 bound by the x axis, x=1 and x=5 is 125/3 - 13/3 = 112/3.

We know by ploting the graphs that y=4x is above y=x- 2x + 5. Hence, to find the area between these two lines is 48 - 112/3 = 32/3.

Rory P. A Level Further Mathematics  tutor, A Level Maths tutor, GCSE...

1 year ago

Answered by Rory, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

182 SUBJECT SPECIALISTS

£20 /hr

Brodie W.

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, Economics

Maths
Economics

“About Me I am a second year economics student from St Aidan’s College, Durham University . Online tutoring is a new experience for me, but I am as keen to learn as I hope you are. I havepassion for all things economics and maths relate...”

£22 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“About Me: I study General Engineering at the University of Durham. I have always enjoyed the maths and science subjects, and hope to help students who also share my love for them too! I have experience in working with young pupils and...”

£20 /hr

Viktoriya L.

Degree: accounting and finance (Bachelors) - LSE University

Subjects offered: Maths, Russian+ 5 more

Maths
Russian
Mandarin
History
Economics
Accounting
-Personal Statements-

“Hello, My name is Viktoriya. I am a first year student at the London school of Economics and Poliical science studying accounting and finance. I am passionate about maths and finance in particular and wish to convey this passion to yo...”

About the author

Rory P.

Currently unavailable: until 04/01/2016

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I am currently reading Mathematics at Imperial College London. I’m warm, patient, reliable but most of all, enthusiastic. My tutoring aim is to make you, the tutee, enjoy Maths and deliver exam success. Throughout sixth form, I helped...”

You may also like...

Other A Level Maths questions

Some videos I've made

Differentiate expressions of form Ax^b where A and b are constants and x is a variable

How do we solve a second order, homogeneous, linear differential equation?

How does one show that x^2 + x + 1 > 0 for all values of x?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok